Analytical study of three-dimensional flexural vibration of micro-rotating shafts with eccentricity utilizing the strain gradient theory

摘要

In this work, some vibrational response parameters of strain gradient based micro-spinning Rayleigh beams with mass eccentricity distribution are investigated within infinitesimal deformation conditions. Governing equations of motion are derived utilizing the Hamilton's principle. The gyroscopic effects and rotary inertia are both included in the formulation. By applying the Galerkin method, analytical expressions for natural frequencies of the micro beam in forward and backward whirl motions are obtained. In addition, an expression for the vibrational amplitude of the micro-beam due to mass eccentricity distribution is determined. Some numerical results are presented to study the effect of higher-order material properties on vibrational characteristics of micro-spinning beams with mass eccentricity.